Une méthode nouvelle autour de la conjecture abc

This paper is the first in a series of four devoted to the abc conjecture, the Rie-mann Hypothesis, Fermat-Wiles Theorem and its extensions, Fermat Numbers and their generalizations. We propose here a method of solving the conjecture abc based on 3 well-established properties of numbers : the sequence of successive odd numbers up to a given bound, the property of the logarithmic function in the interval ]0,1[ and the condition necessary to talk about the conjecture. This method offers the following triple interest : it solves the abc conjecture by determining the associated constant ; it solves a stronger version of the representation of even numbers as the sum which implies the Goldbach conjecture and the second Hardy-Littlewood conjecture ; it elaborates the essential elements for the demonstration of Riemann Hypothesis, of Lemoine's conjecture, and of twin primes conjectures for which it provides a lower bound on π 2. This method makes it possible to integrate into a single a large set of problems including the abc conjecture and the Riemann Hypothesis. This is matter to follow